To have a buffer with a pH of 2.50, what volume of 0.510 M NaOH must be added to 100. mL of 0.230M H3PO4?

To calculate the volume of 0.510 M NaOH needed to make a buffer with a pH of 2.50, we need to use the Henderson-Hasselbalch equation and the concept of buffer equations.

The Henderson-Hasselbalch equation is given by:

pH = pKa + log([A-]/[HA])

In this case, H3PO4 acts as an acid (HA) and its conjugate base (A-) is H2PO4-.

The pKa for H3PO4 is the negative logarithm of the acid dissociation constant for the first ionization, which is approximately 2.15.

Now, let's calculate the moles of H3PO4 present in the 100 mL solution:

moles of H3PO4 = concentration of H3PO4 * volume of solution
= 0.230 M * 0.100 L
= 0.023 moles of H3PO4

According to the Henderson-Hasselbalch equation, we can rewrite it as:

2.50 = 2.15 + log([A-]/[HA])

To calculate the ratio [A-]/[HA], we will consider the dissociation of H3PO4:

H3PO4 → H+ + H2PO4-

From the balanced equation, we know that for every one molecule of H3PO4 that dissociates, one H+ ion and one H2PO4- ion are formed. Therefore, the ratio [A-]/[HA] is 1:1.

Substituting the values into the Henderson-Hasselbalch equation, we get:

2.50 = 2.15 + log(1)

Simplifying, we have:

0.35 = log(1)

Now we need to convert the logarithmic equation back to an exponential equation:

10^0.35 = 1

Using a calculator, we find:

10^0.35 ≈ 2.236

Therefore, the ratio [A-]/[HA] is approximately 2.236:1.

This means that we need 2.236 moles of H2PO4- for every 1 mole of H3PO4 for the buffer to have a pH of 2.50.

Now, let's calculate the volume of 0.510 M NaOH needed to react with the H3PO4 present in the solution:

moles of NaOH needed = moles of H3PO4 * ratio of H2PO4- to H3PO4

moles of NaOH needed = 0.023 moles of H3PO4 * (2.236 moles H2PO4-/ 1 mole H3PO4)
= 0.051 mol of NaOH

Finally, let's calculate the volume of 0.510 M NaOH needed using the molarity equation:

moles of NaOH = concentration of NaOH * volume of NaOH solution

Volume of NaOH solution = moles of NaOH / concentration of NaOH

Volume of NaOH solution = 0.051 mol / 0.510 M
= 0.1 L
= 100 mL

Therefore, you will need to add 100 mL of 0.510 M NaOH to the 100 mL of 0.230 M H3PO4 to obtain a buffer with a pH of 2.50.

To determine the volume of 0.510 M NaOH needed to create a buffer with a pH of 2.50, we must first understand the concept of a buffer solution.

A buffer solution is a solution that resists changes in pH when small amounts of acids or bases are added to it. It consists of a weak acid and its conjugate base (or a weak base and its conjugate acid). The pH of a buffer can be calculated using the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA]),

where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.

In this case, the weak acid is H3PO4 (phosphoric acid), and we want to create a buffer with a pH of 2.50. We need to find the volume of NaOH needed to react with the H3PO4 and create the desired pH.

First, calculate the pKa of phosphoric acid (H3PO4). The pKa values are often provided in reference sources, and for phosphoric acid, it is approximately 2.15. We can use this value since it falls within an acceptable range for approximation.

Next, use the Henderson-Hasselbalch equation to determine the ratio of [A-]/[HA] at the desired pH:

2.50 = 2.15 + log([A-]/[HA]).

Now, rearrange the equation to solve for [A-]/[HA]:

log([A-]/[HA]) = 2.50 - 2.15,

[A-]/[HA] = 10^(2.50 - 2.15),

[A-]/[HA] = 10^0.35.

[A-]/[HA] = 2.24.

Since phosphoric acid is a triprotic acid, it will react with NaOH in a 1:1 molar ratio. This means that for every mole of H3PO4, we need one mole of NaOH.

Now, let's calculate the moles of H3PO4 in the 100. mL of 0.230 M solution:

moles of H3PO4 = volume (L) x concentration (mol/L),

moles of H3PO4 = (100 mL / 1000) L x 0.230 mol/L,

moles of H3PO4 = 0.023 mol.

Since the moles of H3PO4 and NaOH are equal, we need 0.023 mol of NaOH.

Lastly, calculate the volume of 0.510 M NaOH needed to obtain 0.023 mol:

volume of NaOH (L) = moles / concentration,

volume of NaOH (L) = 0.023 mol / 0.510 mol/L.

Convert the volume to milliliters:

volume of NaOH (mL) = (0.023 mol / 0.510 mol/L) x 1000mL/L.

Therefore, you would need approximately 45.1 mL of 0.510 M NaOH to add to 100 mL of 0.230 M H3PO4 to create a buffer solution with a pH of 2.50.